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Sindrei
17 days ago
7

Fill in the missing reason in the following two-column proof for the following information. Given: K is the midpoint of segment

JL; KL = 14 Prove: JK = 14 StatementReason K is the midpoint of JL; KL = 14Given JK = KL? JK = 14Substitution
Mathematics
2 answers:
Svet_ta [12.7K]17 days ago
4 0
To complete the proof as follows: K is the midpoint of JL, and KL is stated to be equal to 14. The goal is to establish that JK equals 14. The proof starts by noting that K is the midpoint of segment JL, as given. The next assertion is that KL equals 14, also given. Following that, JK is deduced to equal KL, under the definition of midpoint. Since JK and KL both equal 14, we can apply the transitive property, concluding that JK equals 14, proving our statement.
lawyer [12.5K]17 days ago
4 0
It is given that K represents the midpoint of line segment JL, and KL measures 14. We must demonstrate that JK is also 14. Since K is established as the midpoint of JL and KL equals 14, it follows from the definition of midpoint that JK must also equal KL. Hence, JK is found to be 14 due to the transitive property.
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Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed

t = time

Formula connecting D, v, and t:

D=v\cdot t

Part A.

Steve's speed: v=3.5\ mph

Distance: a minimum of 21 miles

Time: unknown, so

3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6

It would require Steve a minimum of 6 hours to traverse at least 21 miles on Day 1.

Part B.

Mercedes's speed: v_M=2.4\ mph

Elijah's speed: v_E=3.2\ mph

Elijah's Distance walked: D_E miles

Mercedes's Distance walked: D_M miles

Time: x hours

Mercedes is 2 miles ahead, therefore

D_E=3.2x\\ \\D_M=2.4x+2

Elijah will trail behind until

D_E

In 2.5 hours, Elijah will close the gap on Mercedes, and in less than 2.5 hours, Elijah will trail behind her.

Part C.

Aubrey's speed: v_M=3\ mph

Elijah's speed: v_E=3.2\ mph

Elijah's Distance walked: D_E miles

Aubrey's Distance walked: D_A miles

Time: x hours

At the beginning of Day 3, Elijah starts from Mile 42, while Aubrey begins at Mile 42.5.

D_E=42+3.2x\\ \\D_A=42.5+3x

Elijah will be ahead of Aubrey when

D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours

In 2.5 hours, Elijah will surpass Aubrey, and after more than 2.5 hours, Elijah will outpace Aubrey.

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1 month ago
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